Theoretical Relations Between Static Strength and Lifetime Distributions of Composites: An Evaluation

1984 ◽  
Vol 6 (4) ◽  
pp. 164 ◽  
Author(s):  
WW Feng ◽  
KL Reifsnider ◽  
GP Sendeckyj ◽  
TT Chiao ◽  
W Steve Johnson ◽  
...  
Keyword(s):  
Static Strength ◽  
Lifetime Distributions

Recursions and limit theorems for the strength and lifetime distributions of a fibrous composite

1987 ◽  
Vol 24 (01) ◽  
pp. 137-159 ◽  
Author(s):  
Chia-Chyuan Kuo ◽  
S. Leigh Phoenix
Keyword(s):  
Distribution Function ◽  
Limit Theorem ◽  
Fibrous Composite ◽  
Probability Model ◽  
Failure Process ◽  
Static Strength ◽  
Fatigue Lifetime ◽  
Lifetime Distributions ◽  
The Matrix ◽  
A New Technique

A composite material is a parallel arrangement of stiff brittle fibers in a flexible matrix. Under load fibers fail, and the loads of failed fibers are locally redistributed onto nearby survivors through the matrix. In this paper we develop a new technique for computing the probability of failure under a previously studied model of the failure process. A recursion and limit theorem are obtained which apply separately to static strength and fatigue lifetime depending on the composite loading and the probability model for the failure of individual fibers under their own loads. The limit theorem yields an approximation for the distribution function for composite lifetime which is of the form 1 – [1 – W(t)] mn where W(t) is a characteristic distribution function and mn is the composite volume, reflecting a size effect. A similar result holds also for static strength. In both cases such a result was conjectured several years ago. This limit theorem is obtained from the recursion upon applying a key theorem in the theory of the renewal equation. In the proofs three technical conditions arise which must be verified in specific applications. In the case of static strength these conditions are quite easy to verify, but in the case of fatigue lifetime the verification is generally difficult, and entails considerable numerical computation.

Recursions and limit theorems for the strength and lifetime distributions of a fibrous composite

1987 ◽  
Vol 24 (1) ◽  
pp. 137-159 ◽  
Author(s):  
Chia-Chyuan Kuo ◽  
S. Leigh Phoenix
Keyword(s):  
Distribution Function ◽  
Limit Theorem ◽  
Fibrous Composite ◽  
Probability Model ◽  
Failure Process ◽  
Static Strength ◽  
Fatigue Lifetime ◽  
Lifetime Distributions ◽  
The Matrix ◽  
A New Technique

A composite material is a parallel arrangement of stiff brittle fibers in a flexible matrix. Under load fibers fail, and the loads of failed fibers are locally redistributed onto nearby survivors through the matrix. In this paper we develop a new technique for computing the probability of failure under a previously studied model of the failure process. A recursion and limit theorem are obtained which apply separately to static strength and fatigue lifetime depending on the composite loading and the probability model for the failure of individual fibers under their own loads. The limit theorem yields an approximation for the distribution function for composite lifetime which is of the form 1 – [1 – W(t)]mn where W(t) is a characteristic distribution function and mn is the composite volume, reflecting a size effect. A similar result holds also for static strength. In both cases such a result was conjectured several years ago. This limit theorem is obtained from the recursion upon applying a key theorem in the theory of the renewal equation. In the proofs three technical conditions arise which must be verified in specific applications. In the case of static strength these conditions are quite easy to verify, but in the case of fatigue lifetime the verification is generally difficult, and entails considerable numerical computation.

ALCOA 7150-T7751 and T77511

Alloy Digest ◽  
2015 ◽  
Vol 64 (4) ◽  
Keyword(s):  
Compressive Strength ◽  
Corrosion Resistance ◽  
Tensile Properties ◽  
High Strength ◽  
Static Strength ◽  
Corrosion Resistant ◽  
Overaged Condition

Abstract This producer has pioneered the development of the -T77 temper, a high strength corrosion resistant temper for Alloy 7150 plate and extrusions. Alloy 7150-T77 provides weight savings opportunities in structure governed by static strength requirements but where "overaged" condition corrosion resistance is required. This datasheet provides information on composition, tensile properties, and compressive strength. It also includes information on corrosion resistance as well as forming. Filing Code: Al-442. Producer or source: Alcoa Mill Products Inc..

scholarly journals The use of flat-ended projectiles for determining dynamic yield stress - II. Tests on various metallic materials

1948 ◽  
Vol 194 (1038) ◽  
pp. 300-322 ◽  
Keyword(s):  
Yield Strength ◽  
Dynamic Strength ◽  
Soft Materials ◽  
Static Strength ◽  
Compressive Yield Strength ◽  
Dynamic Tests ◽  
Pure Lead ◽  
Permanent Strain ◽  
Yield Values ◽  
Static Conditions

A description is given of the experimental technique devised to apply the method outlined theoretically in part I to the measurement of the dynamic compressive yield strength of various steels, duralumin, copper, lead, iron and silver. A polished piece of armour steel was employed as a target, and cylindrical specimens were fired at it at various measured velocities from Service weapons. The distance between the weapon and target was made short to ensure normal impact, and apparatus was devised for the precise measurement of striking velocity over this short range. The dynamic compressive yield strength was computed from the density of the specimen, the striking velocity, and from measurements of the dimensions of the test piece before and after test. Details are given of the accuracy of the various measurements, and of their effect on the values of yield strength. The method was found to be inaccurate at low and high velocities. For instance, with mild steel, satisfactory results were only obtainable within the range 400 to 2500 ft. /sec. The range of velocities within which satisfactory results could be obtained varied with the quality of the material tested, soft metals giving results within a much lower range than that necessary for harder materials. Because of its failure at low velocities, the method could not be employed to bridge the gap between static and dynamic tests. The rate of strain employed in the dynamic tests could not be measured, but was estimated to be of the order of 10,000 in. /in. /sec. With the materials tested little change of dynamic strength occurred within the range of striking velocities employed, probably because the rate of strain did not vary to any great extent with the striking velocity. Within the range of weapons available, that is, from a 0·303 in. rifle up to a 13 pdr. gun (calibre 3·12 in.), little change of dynamic strength occurred with alteration of the initial dimensions of the specimens, probably because the corresponding change of rate of strain was not large. In general, the dynamic compressive yield strength S was greater than the static strength Y represented by the compressive stress giving 0·2% permanent strain. For steels of various types, regardless of chemical composition and heat treatment, there was a relation between S / Y and the static strength Y , the ratio decreasing from approximately 3 when Y was 20 tons/sq. in. to 1 when Y was 120 tons/sq. in. A similar relation occurred with duralumin, S / Y varying from 2·5 at Y = 8 tons/sq. in. to 1·4 at Y = 25 tons/sq. in. Dynamic compressive yield values were obtained for soft materials such as pure lead, copper and Armco iron, which, under static conditions, gave no definite yield values. A plot of the unstrained length of the specimen X , expressed as X / L (where L = initial overall length), versus the final overall length L 1 , expressed as L 1 / L , was made for the various materials. Any specified value of X / L was associated with greater values of L 1 / L for the more ductile materials, such as copper and lead, than for the brittle materials, such as armour plate and duralumin.

scholarly journals Semiparametric likelihood inference for heterogeneous survival data under double truncation based on a Poisson birth process

2021 ◽  
Author(s):  
Achim Dörre
Keyword(s):  
Survival Data ◽  
Process Model ◽  
Optimization Method ◽  
Finite Sample ◽  
Birth Process ◽  
Dimensional Parameter ◽  
Lifetime Distributions ◽  
Computational Performance ◽  
Semiparametric Likelihood ◽  
Double Truncation

AbstractWe study a selective sampling scheme in which survival data are observed during a data collection period if and only if a specific failure event is experienced. Individual units belong to one of a finite number of subpopulations, which may exhibit different survival behaviour, and thus cause heterogeneity. Based on a Poisson process model for individual emergence of population units, we derive a semiparametric likelihood model, in which the birth distribution is modeled nonparametrically and the lifetime distributions parametrically, and define maximum likelihood estimators. We propose a Newton–Raphson-type optimization method to address numerical challenges caused by the high-dimensional parameter space. The finite-sample properties and computational performance of the proposed algorithms are assessed in a simulation study. Personal insolvencies are studied as a special case of double truncation and we fit the semiparametric model to a medium-sized dataset to estimate the mean age at insolvency and the birth distribution of the underlying population.

Insensitivity of steady-state distributions of generalized semi-Markov processes by speeds

1978 ◽  
Vol 10 (04) ◽  
pp. 836-851 ◽  
Author(s):  
R. Schassberger
Keyword(s):  
Steady State ◽  
General System ◽  
State Distribution ◽  
Lifetime Distributions ◽  
State Dependent ◽  
Semi Markov Process ◽  
Semi Markov Processes ◽  
Infinite State ◽  
State Case ◽  
Residual Lifetimes

A generalized semi-Markov process with speeds describes the fluctuation, in time, of the state of a certain general system involving, at any given time, one or more living components, whose residual lifetimes are being reduced at state-dependent speeds. Conditions are given for the stationary state distribution, when it exists, to depend only on the means of some of the lifetime distributions, not their exact shapes. This generalizes results of König and Jansen, particularly to the infinite-state case.

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